Full Time

Yes, you can pursue CWA course along with your full time job.
Just make sure sure that you spend enough time on your studies, as it would not be as easy as doing a degree course from college.

Dear Mr. Parth,
Yes, you're eligible for PhD from Mumbai University.
Please keep some important guidelines in mind, if you want to pursue this course:
1. You must have a Master's degree from a recognized university with a minimum aggregate of 55 percent marks.
2. Admission to PhD courses is done through Common Entrance Test namely PET (PhD Entrance Test).

Yes, it is a full-time course.
Refer to the link for details: https://www.shiksha.com/teaching-education/course/integrated-b-ed-m-ed-mahatma-gandhi-antarrashtriya-hindi-vishwavidyalaya-wardha-273237.

Definitely, you can.
And it's good that you are opting for hotel management as there is a tremendous growth potential in this field.

Yes, you are. You can give management entrance tests like CAT, NMAT, MAT, SNAP, XAT, etc.

There are many schools which offer a joint degree in architecture and a regular MBA. Yale School of Architecture is one of them. However, in India, it is not legal to pursue two regular courses according to the guidelines laid down by the UGC. Hence, you should pursue your options abroad.